Definition 1 (Bregman divergence [1]}) 
For a mirror map \(\psi \) , the Bregman divergence \(D_{\psi }\left(\cdot ,\cdot \right)\)  associated to \(\psi \)  is defined as
\(D_{\psi }\left(x,y\right):= \psi (x)-\psi (y) -\left\langle \nabla \psi (y),~ x-y \right\rangle ,\qquad \forall x,y\in \mathbb {R}^n\,.\) 

